Battery Discharge

1. The problem statement, all variables and given/known data
i have to do a scientific research about finding the best batteries specifications. for this case the battery should last long as possible . there are 3 characteristics : Voltage , Capacity and inner resistance .
i have measured voltage over the time. when i used smaller resistances the voltage decreases faster. why?
when i first plug in the battery the change is significant. why it happens this way? i searched the internet and find out duracell's discharge graph. in their graph also the first change is significant.

i used a 9v battery and measured it until the voltage is decreased to 7.9 and then i unplugged it. after a while i did the same measurement again (but with different voltmeters) and saw that the initial voltage was 8.6? how can this happen? or is it a meaurement problem?

I found that a formula , known as Peukert's Law. this law is used to calculate the discharge time but i didnt get the rated and the actual thing.
Thank you for everything:)

I used a 9v battery and measured it until the voltage is decreased to 7.9 and then i unplugged it. after a while i did the same measurement again (but with different voltmeters) and saw that the initial voltage was 8.6? how can this happen?

Batteries can "recover" somewhat when not outputting current (it's related to temperature and internal chemical changes that occur over time.